Homework Grading: Completion vs. Accuracy

I had a discussion with my mentor teacher the other day about how she grades her homework. Most of the homework she only grades for completion, so if you've done all the problems and have the proper type of work shown you get 10 points. From there you lose points if you have problems missing or incomplete. If you really struggle with a problem and just can't figure out how to do it, you can write a question like "How do I use a proportion to solve this problem?" and still get credit for doing the problem. The reason my mentor teacher said she grades this way is because it allows students to feel comfortable making mistakes and it helps put student errors and misunderstandings on the table for discussion. As we talked about in my methods class, sometimes student errors can be a more valuable discussion tool than discussing only the "correct" method. If you only grade for accuracy you force students to be "correct" on every problem and you miss out on key discussion points and the chance to clear up student misconceptions. I think grading for completion can be an extremely useful tool. However, I think that every once in a while you need to grade for accuracy, otherwise the students might get complacent with turning in just incomplete material or material that is worked out wrong. Plus grading for accuracy every now and then helps them be prepared for quizzes and tests. By mixing up the grading styles and not telling the students how they all will be graded it keeps them honest and having to do every problem.